Tunable in-plane topologically protected edge waves in continuum Kagome lattices

In this paper, we report the evidence of topologically protected edge waves (TPEWs) in continuum Kagome lattice. According to the bulk edge correspondence principle, such edge states are inherently linked with the topological characteristics of the material band structure and can, therefore, be predicted evaluating the associated topological invariant. Due to the non-trivial band structures shown in the context of quantum valley Hall effect, TPEWs are supported at the interface between two lattices characterized by different valley Chern numbers. The break of lattice symmetry is obtained here, in contrast with other similar works in continuum elastic structures, biasing in the stiffness properties of the unit cell, instead of manipulating mass at sublattice points. This opens new promising possibilities related to waveguide tunability and wave propagation control, exploiting the established techniques for stiffness modulation in elastic structures. A sensitivity analysis of robustness of the supported energy transport is provided, showing the amount of de-localized disorder the waveguide is immune to, and how performances are affected by perturbations in the nominal parameters of the lattice.